Tribulus is a food supplement that some athletes use to enhance performance. A study on the effects of this supplement involved randomly assigning 20 athletes to take the supplement for a 20 day period and comparing various characteristics to 12 similar athletes who were not given Tribulus. One of the measurements was anaerobic alactic muscular power (AAMP) where the Tribulus group showed a mean performance of 1305.6 with a standard deviation of 177.3 while the control group had a mean AAMP of 1255.9 with a standard deviation of 66.8. (a) Test whether the data provide evidence that mean AAMP is higher for athletes using Tribulus compared to those not using the supplement. (b) The authors of the study also report that the mean AAMP of the 20 subjects in the experimental group before they started the Tribulus supplements was 1215.5 with a standard deviation of 146.6. Explain why this is not sufficient information to let us test for a difference in means before and after using the supplement.

(a) Test whether the data provide evidence that mean AAMP is higher for athletes using Tribulus compared to those not using the supplement. 

(b) The authors of the study also report that the mean AAMP of the 20 subjects in the experimental group before they started the Tribulus supplements was 1215.5 with a standard deviation of 146.6. Explain why this is not sufficient information to let us test for a difference in means before and after using the supplement.